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Simplifying 0.5x2 + 3x = 8 Reorder the terms: 3x + 0.5x2 = 8 Solving 3x + 0.5x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 3x + 0.5x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 3x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -16 + 6x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 6x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 6x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 6x + x2 = 0 + 16 6x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 6x + x2 = 16 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 16 + 9 Reorder the terms: 9 + 6x + x2 = 16 + 9 Combine like terms: 16 + 9 = 25 9 + 6x + x2 = 25 Factor a perfect square on the left side: (x + 3)(x + 3) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + 3) equal to 5 and -5.Subproblem 1
x + 3 = 5 Simplifying x + 3 = 5 Reorder the terms: 3 + x = 5 Solving 3 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5 + -3 x = 5 + -3 Combine like terms: 5 + -3 = 2 x = 2 Simplifying x = 2Subproblem 2
x + 3 = -5 Simplifying x + 3 = -5 Reorder the terms: 3 + x = -5 Solving 3 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5 + -3 x = -5 + -3 Combine like terms: -5 + -3 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -8}
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